Abstract: We considered  six types of algebras generated by linear transformations of a δ-Lie supertriple system T: the derivation algebra Der(T)， the quasiderivation algebra QDer(T)， the generalized derivation algebra GDer(T)， the central derivation algebra ZDer(T)， the centroid algebra C(T)， and the quasicentroid algebra QC(T). We first proved that ZDer(T) was an ideal of Der(T) and ZDer(T)Der(T)QDer(T)GDer(T)End(T), then obtained that ［Der(T),C(T)］C(T), ［QDer(T),QC(T)］QC(T), ［QC(T),QC(T)\]QDer(T), QDer(T)+QC(T)=GDer(T) and［C(T),QC(T)］End(T,Z(T)). Moreover, we proved that if a δ-Lie supertriple system was decomposable, then its generalized derivation algebra, quasiderivation algebra, centroid algebra, and quasicentroid algebra also had corresponding decomposition, respectively.

Key words: δ-Lie supertriple system, Lie supertriple system, quasicentroids, generalized derivation